Section: New Results

Towards a Stochastic Linear Logic for Biological Computation

Participants : Kaustuv Chaudhuri, Joëlle Despeyroux.

In previous work  [35] , Joëlle Despeyroux and Kaustuv Chaudhuri have given an encoding of the synchronous stochastic $\pi$-calculus in a hybrid extension of intuitionistic linear logic (called HyLL). Precisely, they have shown that focused partial sequent derivations in the encoding are in bijection with stochastic traces. The modal worlds are used to represent the rates of stochastic interactions, and the connectives of hybrid logic are used to represent the constraints in the stochastic transition rules.

One of the most successful applications of the stochastic $\pi$-calculus has been in representing signal transduction networks in cellular biology. An interesting application of this work would therefore be the direct representations of biological processes in HyLL, the original motivation for this line of investigation.

This year, we have worked on specifying some simple examples of regulatory gene networks, together with basic properties of them—such as stability or oscillation—in HyLL. This is ongoing work in collaboration with Gilles Bernot's team at Nice-Sophia university.